Abstract

We explore the use of diffuse optical tomography (DOT) for the recovery of 3D tubular shapes representing vascular structures in breast tissue. Using a parametric level set method (PaLS) our method incorporates the connectedness of vascular structures in breast tissue to reconstruct shape and absorption values from severely limited data sets. The approach is based on a decomposition of the unknown structure into a series of two dimensional slices. Using a simplified physical model that ignores 3D effects of the complete structure, we develop a novel inter-slice regularization strategy to obtain global regularity. We report on simulated and experimental reconstructions using realistic optical contrasts where our method provides a more accurate estimate compared to an unregularized approach and a pixel based reconstruction.

© 2013 OSA

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  1. Y. Yang, A. Sassaroli, D. K. Chen, M. J. Homer, R. A. Graham, and S. Fantini, “Near-infrared, broad-band spectral imaging of the human breast for quantitative oximetry: applications to healthy and cancerous breasts,” J. Innov. Opt. Health Sci.3, 267–277 (2010).
    [CrossRef]
  2. A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous diffuse optical tomography,” Opt. Lett.29, 256–258 (2004).
    [CrossRef] [PubMed]
  3. S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
    [CrossRef]
  4. P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express15, 8043–8058 (2007).
    [CrossRef] [PubMed]
  5. Y. Bresler, J. A. Fessler, and A. Macovski, “A bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain,” IEEE Trans. Pattern Anal. Mach. Intell.2, 840–858 (1989).
    [CrossRef]
  6. R. A. Jesinger, G. E. Lattin, E. A. Ballard, S. M. Zelasko, and L. M. Glassman, “Vascular abnormalities of the breast: arterial and venous disorders, vascular masses, and mimic lesions with radiologic-pathologic correlation,” Radiographics31, E117–E136 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  21. T. Chan and L. Vese, “Active contours without edges,” Inverse Probl.10(2), 266–277 (2001).
  22. S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2002)
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    [CrossRef] [PubMed]
  26. S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
    [CrossRef] [PubMed]
  27. O. Semerci and E. L. Miller, “A parametric level set approach to simultaneous object identification and background reconstruction for dual energy computed tomography,” IEEE Trans. Image Process.21, 2719–2734 (2012).
    [CrossRef] [PubMed]
  28. T. Tarvainen, V. Kolehmainen, J. P. Kaipio, and S. R. Arridge, “Corrections to linear methods for diffuse optical tomography using approximation error modelling,” Biomed. Opt. Express1, 209–222 (2010).
    [CrossRef]
  29. P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, 1st ed. (SIAM,1997).

2012 (2)

O. Semerci and E. L. Miller, “A parametric level set approach to simultaneous object identification and background reconstruction for dual energy computed tomography,” IEEE Trans. Image Process.21, 2719–2734 (2012).
[CrossRef] [PubMed]

F. Larusson, S. Fantini, and E. L. Miller, “Parametric level set reconstruction methods for hyperspectral diffuse optical tomography,” Biomed. Opt. Express3, 1006–1024 (2012).
[CrossRef] [PubMed]

2011 (4)

A. Aghasi, M. Kilmer, and E. L. Miller, “Parametric level set methods for inverse problems,” SIAM J. Imaging Sci.4, 618–650 (2011).
[CrossRef]

R. A. Jesinger, G. E. Lattin, E. A. Ballard, S. M. Zelasko, and L. M. Glassman, “Vascular abnormalities of the breast: arterial and venous disorders, vascular masses, and mimic lesions with radiologic-pathologic correlation,” Radiographics31, E117–E136 (2011).
[CrossRef] [PubMed]

S. Fantini and A. Sassaroli, “Near-infrared optical mammography for breast cancer detection with intrinsic contrast,” Ann. Biomed. Eng.40, 398–407(2011).
[CrossRef] [PubMed]

F. Larusson, S. Fantini, and E. L. Miller, “Hyperspectral image reconstruction for diffuse optical tomography,” Biomed. Opt. Express2, 947–965 (2011).
[CrossRef]

2010 (3)

Y. Yang, A. Sassaroli, D. K. Chen, M. J. Homer, R. A. Graham, and S. Fantini, “Near-infrared, broad-band spectral imaging of the human breast for quantitative oximetry: applications to healthy and cancerous breasts,” J. Innov. Opt. Health Sci.3, 267–277 (2010).
[CrossRef]

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

T. Tarvainen, V. Kolehmainen, J. P. Kaipio, and S. R. Arridge, “Corrections to linear methods for diffuse optical tomography using approximation error modelling,” Biomed. Opt. Express1, 209–222 (2010).
[CrossRef]

2008 (1)

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

2007 (1)

2004 (3)

2003 (1)

2002 (1)

M. Belge, M. E. Kilmer, and E. L. Miller, “Efficient determination of multiple regularization parameters in a generalized l-curve framework,” Inverse Probl.18, 1161–1183 (2002).
[CrossRef]

2001 (2)

2000 (1)

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techinques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol.45, 1051–1069 (2000).
[CrossRef] [PubMed]

1999 (1)

1997 (1)

1989 (1)

Y. Bresler, J. A. Fessler, and A. Macovski, “A bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain,” IEEE Trans. Pattern Anal. Mach. Intell.2, 840–858 (1989).
[CrossRef]

A., F.

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Aghasi, A.

A. Aghasi, M. Kilmer, and E. L. Miller, “Parametric level set methods for inverse problems,” SIAM J. Imaging Sci.4, 618–650 (2011).
[CrossRef]

Arridge, S. R.

Bakker, L.

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

Ballard, E. A.

R. A. Jesinger, G. E. Lattin, E. A. Ballard, S. M. Zelasko, and L. M. Glassman, “Vascular abnormalities of the breast: arterial and venous disorders, vascular masses, and mimic lesions with radiologic-pathologic correlation,” Radiographics31, E117–E136 (2011).
[CrossRef] [PubMed]

Barbaro, A.

Belge, M.

M. Belge, M. E. Kilmer, and E. L. Miller, “Efficient determination of multiple regularization parameters in a generalized l-curve framework,” Inverse Probl.18, 1161–1183 (2002).
[CrossRef]

Boas, D. A.

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous diffuse optical tomography,” Opt. Lett.29, 256–258 (2004).
[CrossRef] [PubMed]

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techinques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol.45, 1051–1069 (2000).
[CrossRef] [PubMed]

D. A. Boas, “A fundamental limitation of linearized algorithms for diffuse optical tomography,” Opt. Express1, 404–413 (1997).
[CrossRef] [PubMed]

Boas, David

Brendel, B.

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

Bresler, Y.

Y. Bresler, J. A. Fessler, and A. Macovski, “A bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain,” IEEE Trans. Pattern Anal. Mach. Intell.2, 840–858 (1989).
[CrossRef]

Brooks, D. H.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techinques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol.45, 1051–1069 (2000).
[CrossRef] [PubMed]

Carpenter, C. M.

Chan, T.

T. Chan and L. Vese, “Active contours without edges,” Inverse Probl.10(2), 266–277 (2001).

Chen, D. K.

Y. Yang, A. Sassaroli, D. K. Chen, M. J. Homer, R. A. Graham, and S. Fantini, “Near-infrared, broad-band spectral imaging of the human breast for quantitative oximetry: applications to healthy and cancerous breasts,” J. Innov. Opt. Health Sci.3, 267–277 (2010).
[CrossRef]

Choe, R.

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Corlu, A.

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Culver, J. P.

Dehghani, H.

Del Bianco, S.

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media, 1st ed. (SPIE, 2009).

DiMarzio, C. A.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techinques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol.45, 1051–1069 (2000).
[CrossRef] [PubMed]

Elias, S.

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

Fantini, S.

F. Larusson, S. Fantini, and E. L. Miller, “Parametric level set reconstruction methods for hyperspectral diffuse optical tomography,” Biomed. Opt. Express3, 1006–1024 (2012).
[CrossRef] [PubMed]

F. Larusson, S. Fantini, and E. L. Miller, “Hyperspectral image reconstruction for diffuse optical tomography,” Biomed. Opt. Express2, 947–965 (2011).
[CrossRef]

S. Fantini and A. Sassaroli, “Near-infrared optical mammography for breast cancer detection with intrinsic contrast,” Ann. Biomed. Eng.40, 398–407(2011).
[CrossRef] [PubMed]

Y. Yang, A. Sassaroli, D. K. Chen, M. J. Homer, R. A. Graham, and S. Fantini, “Near-infrared, broad-band spectral imaging of the human breast for quantitative oximetry: applications to healthy and cancerous breasts,” J. Innov. Opt. Health Sci.3, 267–277 (2010).
[CrossRef]

Fedkiw, R.

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2002)

Fels, L.

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

Fessler, J. A.

Y. Bresler, J. A. Fessler, and A. Macovski, “A bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain,” IEEE Trans. Pattern Anal. Mach. Intell.2, 840–858 (1989).
[CrossRef]

Freifelder, R.

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Gaudette, R. J.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techinques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol.45, 1051–1069 (2000).
[CrossRef] [PubMed]

Gaudette, T.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techinques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol.45, 1051–1069 (2000).
[CrossRef] [PubMed]

Glassman, L. M.

R. A. Jesinger, G. E. Lattin, E. A. Ballard, S. M. Zelasko, and L. M. Glassman, “Vascular abnormalities of the breast: arterial and venous disorders, vascular masses, and mimic lesions with radiologic-pathologic correlation,” Radiographics31, E117–E136 (2011).
[CrossRef] [PubMed]

Graham, R. A.

Y. Yang, A. Sassaroli, D. K. Chen, M. J. Homer, R. A. Graham, and S. Fantini, “Near-infrared, broad-band spectral imaging of the human breast for quantitative oximetry: applications to healthy and cancerous breasts,” J. Innov. Opt. Health Sci.3, 267–277 (2010).
[CrossRef]

Hajjioui, N.

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Hansen, P. C.

P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, 1st ed. (SIAM,1997).

Holboke, M. J.

Homer, M. J.

Y. Yang, A. Sassaroli, D. K. Chen, M. J. Homer, R. A. Graham, and S. Fantini, “Near-infrared, broad-band spectral imaging of the human breast for quantitative oximetry: applications to healthy and cancerous breasts,” J. Innov. Opt. Health Sci.3, 267–277 (2010).
[CrossRef]

Ismaelli, A.

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media, 1st ed. (SPIE, 2009).

Jesinger, R. A.

R. A. Jesinger, G. E. Lattin, E. A. Ballard, S. M. Zelasko, and L. M. Glassman, “Vascular abnormalities of the breast: arterial and venous disorders, vascular masses, and mimic lesions with radiologic-pathologic correlation,” Radiographics31, E117–E136 (2011).
[CrossRef] [PubMed]

Jiang, S.

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express15, 8043–8058 (2007).
[CrossRef] [PubMed]

B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycles changes,” J. Biomed. Opt.9 (2004).
[CrossRef] [PubMed]

Kaipio, J. P.

Karp, J. S.

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Kilmer, M.

A. Aghasi, M. Kilmer, and E. L. Miller, “Parametric level set methods for inverse problems,” SIAM J. Imaging Sci.4, 618–650 (2011).
[CrossRef]

Kilmer, M. E.

M. E. Kilmer, E. L. Miller, A. Barbaro, and David Boas, “Three-dimensional shape-based imaging of absorption perturbation for diffuse optical tomography,” Appl. Opt.42, 3129–3144 (2003).
[CrossRef] [PubMed]

M. Belge, M. E. Kilmer, and E. L. Miller, “Efficient determination of multiple regularization parameters in a generalized l-curve framework,” Inverse Probl.18, 1161–1183 (2002).
[CrossRef]

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techinques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol.45, 1051–1069 (2000).
[CrossRef] [PubMed]

Kogel, C.

B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycles changes,” J. Biomed. Opt.9 (2004).
[CrossRef] [PubMed]

Kolehmainen, V.

Konecky, S. D.

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Larusson, F.

F. Larusson, S. Fantini, and E. L. Miller, “Parametric level set reconstruction methods for hyperspectral diffuse optical tomography,” Biomed. Opt. Express3, 1006–1024 (2012).
[CrossRef] [PubMed]

F. Larusson, S. Fantini, and E. L. Miller, “Hyperspectral image reconstruction for diffuse optical tomography,” Biomed. Opt. Express2, 947–965 (2011).
[CrossRef]

Lattin, G. E.

R. A. Jesinger, G. E. Lattin, E. A. Ballard, S. M. Zelasko, and L. M. Glassman, “Vascular abnormalities of the breast: arterial and venous disorders, vascular masses, and mimic lesions with radiologic-pathologic correlation,” Radiographics31, E117–E136 (2011).
[CrossRef] [PubMed]

Laub, A. J.

A. J. Laub, Matrix Analysis for Scientists and Engineers, 1st ed. (Society for Industrial and Applied Mathematics, 2004),

Lee, K.

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Li, A.

Luijten, P.

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

Macovski, A.

Y. Bresler, J. A. Fessler, and A. Macovski, “A bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain,” IEEE Trans. Pattern Anal. Mach. Intell.2, 840–858 (1989).
[CrossRef]

Madsen, K.

K. Madsen, H. B. Nielsen, and O. Tingleff, “Methods for non-linear least squares problems”, Informatics and Mathematical Modelling, Technical University of Denmark, DTU,Nielsen Lecture Notes (2004).

Mali, W.

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

Mandelis, A.

A. Mandelis, Diffusion-Wave Fields: Mathematical Methods and Green Functions (Springer, 2001), 1st ed.
[CrossRef]

Martelli, F.

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media, 1st ed. (SPIE, 2009).

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Miller, E. L.

F. Larusson, S. Fantini, and E. L. Miller, “Parametric level set reconstruction methods for hyperspectral diffuse optical tomography,” Biomed. Opt. Express3, 1006–1024 (2012).
[CrossRef] [PubMed]

O. Semerci and E. L. Miller, “A parametric level set approach to simultaneous object identification and background reconstruction for dual energy computed tomography,” IEEE Trans. Image Process.21, 2719–2734 (2012).
[CrossRef] [PubMed]

A. Aghasi, M. Kilmer, and E. L. Miller, “Parametric level set methods for inverse problems,” SIAM J. Imaging Sci.4, 618–650 (2011).
[CrossRef]

F. Larusson, S. Fantini, and E. L. Miller, “Hyperspectral image reconstruction for diffuse optical tomography,” Biomed. Opt. Express2, 947–965 (2011).
[CrossRef]

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous diffuse optical tomography,” Opt. Lett.29, 256–258 (2004).
[CrossRef] [PubMed]

M. E. Kilmer, E. L. Miller, A. Barbaro, and David Boas, “Three-dimensional shape-based imaging of absorption perturbation for diffuse optical tomography,” Appl. Opt.42, 3129–3144 (2003).
[CrossRef] [PubMed]

M. Belge, M. E. Kilmer, and E. L. Miller, “Efficient determination of multiple regularization parameters in a generalized l-curve framework,” Inverse Probl.18, 1161–1183 (2002).
[CrossRef]

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techinques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol.45, 1051–1069 (2000).
[CrossRef] [PubMed]

Nachabe, R.

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

Nielsen, H. B.

K. Madsen, H. B. Nielsen, and O. Tingleff, “Methods for non-linear least squares problems”, Informatics and Mathematical Modelling, Technical University of Denmark, DTU,Nielsen Lecture Notes (2004).

Nielsen, T.

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

Ntziachristos, V.

Osher, S.

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2002)

Osterberg, U. L.

Paulsen, K. D.

Pogue, B. W.

Poplack, S. P.

H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: Initial simulation, phantom, and clinical results,” Appl. Opt.42, 135–145 (2004).
[CrossRef]

B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycles changes,” J. Biomed. Opt.9 (2004).
[CrossRef] [PubMed]

Prewitt, J.

Saffer, J. R.

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Sassaroli, A.

S. Fantini and A. Sassaroli, “Near-infrared optical mammography for breast cancer detection with intrinsic contrast,” Ann. Biomed. Eng.40, 398–407(2011).
[CrossRef] [PubMed]

Y. Yang, A. Sassaroli, D. K. Chen, M. J. Homer, R. A. Graham, and S. Fantini, “Near-infrared, broad-band spectral imaging of the human breast for quantitative oximetry: applications to healthy and cancerous breasts,” J. Innov. Opt. Health Sci.3, 267–277 (2010).
[CrossRef]

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O. Semerci and E. L. Miller, “A parametric level set approach to simultaneous object identification and background reconstruction for dual energy computed tomography,” IEEE Trans. Image Process.21, 2719–2734 (2012).
[CrossRef] [PubMed]

Soho, S.

B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycles changes,” J. Biomed. Opt.9 (2004).
[CrossRef] [PubMed]

Song, X.

B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycles changes,” J. Biomed. Opt.9 (2004).
[CrossRef] [PubMed]

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S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Srinivasan, S.

B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycles changes,” J. Biomed. Opt.9 (2004).
[CrossRef] [PubMed]

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Tingleff, O.

K. Madsen, H. B. Nielsen, and O. Tingleff, “Methods for non-linear least squares problems”, Informatics and Mathematical Modelling, Technical University of Denmark, DTU,Nielsen Lecture Notes (2004).

Tosteson, T. D.

B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycles changes,” J. Biomed. Opt.9 (2004).
[CrossRef] [PubMed]

Van Beek, M.

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

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S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

Van der Mark, M.

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

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S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

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T. Chan and L. Vese, “Active contours without edges,” Inverse Probl.10(2), 266–277 (2001).

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[CrossRef]

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S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Wiethoff, A.

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

Yalavarthy, P. K.

Yang, Y.

Y. Yang, A. Sassaroli, D. K. Chen, M. J. Homer, R. A. Graham, and S. Fantini, “Near-infrared, broad-band spectral imaging of the human breast for quantitative oximetry: applications to healthy and cancerous breasts,” J. Innov. Opt. Health Sci.3, 267–277 (2010).
[CrossRef]

Yodh, A. G.

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: A singular-value analysis,” Opt. Lett.26, 701–703 (2001).
[CrossRef]

Zaccanti, G.

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media, 1st ed. (SPIE, 2009).

Zelasko, S. M.

R. A. Jesinger, G. E. Lattin, E. A. Ballard, S. M. Zelasko, and L. M. Glassman, “Vascular abnormalities of the breast: arterial and venous disorders, vascular masses, and mimic lesions with radiologic-pathologic correlation,” Radiographics31, E117–E136 (2011).
[CrossRef] [PubMed]

Zhang, Q.

Ann. Biomed. Eng. (1)

S. Fantini and A. Sassaroli, “Near-infrared optical mammography for breast cancer detection with intrinsic contrast,” Ann. Biomed. Eng.40, 398–407(2011).
[CrossRef] [PubMed]

Appl. Opt. (3)

Biomed. Opt. Express (3)

IEEE Trans. Image Process. (1)

O. Semerci and E. L. Miller, “A parametric level set approach to simultaneous object identification and background reconstruction for dual energy computed tomography,” IEEE Trans. Image Process.21, 2719–2734 (2012).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Y. Bresler, J. A. Fessler, and A. Macovski, “A bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain,” IEEE Trans. Pattern Anal. Mach. Intell.2, 840–858 (1989).
[CrossRef]

Inverse Probl. (2)

T. Chan and L. Vese, “Active contours without edges,” Inverse Probl.10(2), 266–277 (2001).

M. Belge, M. E. Kilmer, and E. L. Miller, “Efficient determination of multiple regularization parameters in a generalized l-curve framework,” Inverse Probl.18, 1161–1183 (2002).
[CrossRef]

J. Biomed. Opt. (1)

B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycles changes,” J. Biomed. Opt.9 (2004).
[CrossRef] [PubMed]

J. Innov. Opt. Health Sci. (1)

Y. Yang, A. Sassaroli, D. K. Chen, M. J. Homer, R. A. Graham, and S. Fantini, “Near-infrared, broad-band spectral imaging of the human breast for quantitative oximetry: applications to healthy and cancerous breasts,” J. Innov. Opt. Health Sci.3, 267–277 (2010).
[CrossRef]

Med. Phys. (1)

S. D. Konecky, R. Choe, A. Corlu, K. Lee, R. Wiener, S. M. Srinivas, J. R. Saffer, R. Freifelder, J. S. Karp, N. Hajjioui, F. A., and A. G. Yodh, “Comparison of diffuse optical tomography of human breast with whole-body and breast-only positron emission tomography,” Med. Phys.35, 446–455 (2008).
[CrossRef] [PubMed]

Mol. Imaging Biol. (1)

S. van de Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. van der Voort, R. Nachabe, M. Van der Mark, M. Van Beek, L. Bakker, L. Fels, S. Elias, P. Luijten, and W. Mali, “A novel fluorescent imaging agent for diffuse optical tomography of the breast: first clinical experience in patients,” Mol. Imaging Biol.12, 343–348, 2010.
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Med. Biol. (1)

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techinques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol.45, 1051–1069 (2000).
[CrossRef] [PubMed]

Radiographics (1)

R. A. Jesinger, G. E. Lattin, E. A. Ballard, S. M. Zelasko, and L. M. Glassman, “Vascular abnormalities of the breast: arterial and venous disorders, vascular masses, and mimic lesions with radiologic-pathologic correlation,” Radiographics31, E117–E136 (2011).
[CrossRef] [PubMed]

SIAM J. Imaging Sci. (1)

A. Aghasi, M. Kilmer, and E. L. Miller, “Parametric level set methods for inverse problems,” SIAM J. Imaging Sci.4, 618–650 (2011).
[CrossRef]

Other (7)

A. Mandelis, Diffusion-Wave Fields: Mathematical Methods and Green Functions (Springer, 2001), 1st ed.
[CrossRef]

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2002)

K. Madsen, H. B. Nielsen, and O. Tingleff, “Methods for non-linear least squares problems”, Informatics and Mathematical Modelling, Technical University of Denmark, DTU,Nielsen Lecture Notes (2004).

C. R. Vogel, Computational Methods for Inverse Problems, 1st ed. (SIAM, 2002).
[CrossRef]

A. J. Laub, Matrix Analysis for Scientists and Engineers, 1st ed. (Society for Industrial and Applied Mathematics, 2004),

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media, 1st ed. (SPIE, 2009).

P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, 1st ed. (SIAM,1997).

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Figures (12)

Fig. 1
Fig. 1

The setup of sources and detectors for simulation reconstructions. Same orientation of axes is used for experimental data. The angle φ represents the angle between the axis of the inclusion, along y in the figure, and the scanning direction, along x in the figure.

Fig. 2
Fig. 2

(a) Definition of domains used for the parametric level-set methods. (b) Example basis functions placed in the imaging medium. The iteration process evolves κi and ψi towards the estimated primitive structure

Fig. 3
Fig. 3

(a) Example L-curve used to select optimal α for the reconstruction in Fig. 7. (b) Ground truth used to generate phantom 1, with multiple overlaying cylinders. (c) Ground truth image used to generate phantom 2, with a single branching structure.

Fig. 4
Fig. 4

Calculated ground truth images for phantom angled at φ = 90° and φ = 30° relative to scanning direction along the x-axis.

Fig. 6
Fig. 6

Reconstruction results from simulated data, phantom 1, with realistic optical contrast, using 2 detectors for each source location. Recovered absorption values are Δμa = 0.015 and Δμa = 0.019, for Fig. (a) and (b), respectively.

Fig. 7
Fig. 7

Reconstruction results from simulated data, phantom 1, with realistic optical contrast, using 10 detectors for each source location. Recovered absorption values are Δμa = 0.021 and Δμa = 0.026, for Fig. (a) and (b), respectively.

Fig. 9
Fig. 9

Reconstruction results from simulated data, phantom 2, using 10 detectors for each source location. Recovered absorption value is Δμa = 0.020.

Fig. 5
Fig. 5

Reconstruction results for a simulated data, phantom 1, with realistic optical contrast. Recovered absorption values are Δμa = 0.018 and Δμa = 0.022, for Fig. (a) and (b), respectively.

Fig. 8
Fig. 8

(a) Slice reconstruction, shown on the bottom, located at y = 5 cm in Fig. 7(b), compared to (b) ground truth, shown on top, demonstrating absorption perturbation, Δμa.

Fig. 10
Fig. 10

Reconstruction results using experimental data and 3 detectors. Inclusions are angled 90° relative to scanning direction, α = 12. Recovered absorption contrast is 2.75, slice image shown in Fig. 12.

Fig. 11
Fig. 11

Reconstruction results using experimental data and 3 detectors. Inclusions are angled 30° relative to scanning direction, α = 80. Recovered absorption contrast is 2.30.

Fig. 12
Fig. 12

Slice reconstruction, shown on the right, located at y = 3 cm in Fig. 10, compared to ground truth, shown on the left, demonstrating absorption contrast.

Tables (2)

Tables Icon

Table 1 Error metrics used to judge image reconstructions for simulated reconstructions.

Tables Icon

Table 2 Error metrics used to judge image reconstructions for experimental reconstructions.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

( 2 + v μ a 0 ( r ) D ) Φ ( r ) = v D δ ( r )
[ 2 + k 0 2 ] Φ s ( r ) = Δ k 2 ( r ) Φ ( r )
Φ s ( r d ) G ( r d , r ) Φ i ( r , r s ) Δ μ a ( r ) d r
[ Φ 1 s Φ 2 s Φ K s ] = [ K 1 0 0 0 K 2 0 0 0 K K ] [ c 1 c 2 c K ] Φ s = Kc
χ ( x , y ) = { 1 if ( x , y ) Ω , 0 if ( x , y ) \ Ω .
c k ( x , y ) = c k a χ k ( x , y ) + [ 1 χ k ( x , y ) ] c k b
χ ( x , y ) = H ( 𝒪 ( r , [ κ , β ] ) τ )
𝒪 ( r , [ κ , β ] ) = i = 1 L κ i ψ i ( β i r r i )
Φ s = K ( θ ) = Kc ( θ )
θ ^ = argmin W ( Φ s Kc ( θ ) 2 2 + α L θ 2
L = L d I
L d = [ 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 ] .
σ m 2 = Ω ( m ) 10 SN R m 10 .
SNR m = 10 log 10 ( Ω ( m ) / Ω ( m ) ) .
ε 1 = W ( K ( θ ) Φ s )
ε 2 = α L θ .
J = [ ε ( θ ) { c 1 a , , c K a , ( κ 1 T , κ K T ) T , ( β 1 T , , β K T ) T , ( r 1 T , , r K T ) T } ]
( J T J + ρ I ) h = J T ε with ρ 0
d s d ( S act , S est ) = 1 N v i 1 { S i act S i est }
d di ( S est , S act ) = 2 | S est S act | | S est | + | S act |
M S E = c c ^ 2 c 2 .
G ( r ) = v 4 π D m = m = + { exp [ μ eff ρ 2 + ( z z m + ) 2 ] ρ 2 + ( z z m + ) 2 exp [ μ eff ρ 2 + ( z z m ) 2 ] ρ 2 + ( z z m ) 2 }

Metrics